Can Cycles nodes use "object coordinates" like blender internal? (or: how can hair-mesh-objects inherit their emitter's texture)?
I have managed to answer my own specific question, but not the more general question. I will explain, but I hope that someone may be able to answer the general form.

To specifically answer my question, deriving the color of a particle hair MESH from its underlying emitter object (in this case, a feather mesh being colored by the bird's texture) in CYCLES (not Blender Internal), I found resolution in Blender Cookie/Kent Trammel's "Piero" tutorial series (video: body feathers #3), with clarification from a previous Blender developer bug-fix request (found here: https://developer.blender.org/T40712).

To derive a particle mesh's diffuse texture from an underlying emitter in Cycles, in the hair's material nodes, add a Texture Coordinate (add > input ) menu, and then an Image texture, as per normal.

However, the key difference is on the Texture Coordinate tab, you have to click "From Dupli", and as the texture image itself, you must select the texture from the underlying emitter. This info is from Kent Trammel's tutorial.

BUT! There is one more issue that can drive someone crazy. Due to some ambiguity in the underlying code in the past few incarnations of Blender (I am using 2.7), the results of "From Dupli" will NOT show up in a preview render. To see the results, a "real" F12 render must be performed!

So, this is the specific answer to the above question.

However, the general question of "object coordinates" remains open, and that is an issue that goes far beyond particles and emitters, toward texturing objects with other objects, or, for instances, controlling texture placement with an Empty.